2.2.76 Problems 7501 to 7600

Table 2.165: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

7501

\begin{align*} x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

20.027

7502

\begin{align*} y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

5.024

7503

\begin{align*} y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

58.343

7504

\begin{align*} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

9.645

7505

\begin{align*} y^{\prime }&=\sqrt {x +y}-1 \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

2.539

7506

\begin{align*} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

4.612

7507

\begin{align*} y^{\prime }&=\left (x -y+5\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

4.546

7508

\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

1.903

7509

\begin{align*} y^{\prime }+\frac {y}{x}&=y^{2} x^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

5.657

7510

\begin{align*} y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2.888

7511

\begin{align*} y^{\prime }&=\frac {2 y}{x}-y^{2} x^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

6.530

7512

\begin{align*} y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

8.941

7513

\begin{align*} x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

4.366

7514

\begin{align*} y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2.416

7515

\begin{align*} r^{\prime }&=r^{2}+\frac {2 r}{t} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

6.971

7516

\begin{align*} y^{\prime }+x y^{3}+y&=0 \\ \end{align*}

[_Bernoulli]

4.316

7517

\begin{align*} x +y-1+\left (-x +y-5\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14.705

7518

\begin{align*} -4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

56.295

7519

\begin{align*} 2 x -y+\left (4 x +y-3\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

26.225

7520

\begin{align*} 2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.428

7521

\begin{align*} y^{\prime }&=\frac {2 y}{x}+\cos \left (\frac {y}{x^{2}}\right ) \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

3.830

7522

\begin{align*} y^{\prime }&=-4 x-y \\ x^{\prime }&=2 x-y \\ \end{align*}

system_of_ODEs

0.430

7523

\begin{align*} y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

11.816

7524

\begin{align*} y^{\prime }&=x^{3} \left (-x +y\right )^{2}+\frac {y}{x} \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Riccati]

4.628

7525

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\ \end{align*}

[_separable]

3.355

7526

\begin{align*} y^{\prime }-4 y&=32 x^{2} \\ \end{align*}

[[_linear, ‘class A‘]]

2.066

7527

\begin{align*} \left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2}&=0 \\ \end{align*}

[_exact, _rational]

3.207

7528

\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\ \end{align*}

[_linear]

3.367

7529

\begin{align*} 2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.769

7530

\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\ \end{align*}

[_separable]

3.613

7531

\begin{align*} y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.804

7532

\begin{align*} x^{2}+y^{2}+3 y y^{\prime } x&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

9.948

7533

\begin{align*} 1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

83.207

7534

\begin{align*} x^{\prime }&=1+\cos \left (t -x\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

4.487

7535

\begin{align*} y^{3}+4 \,{\mathrm e}^{x} y+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

2.766

7536

\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \sin \left (2 x \right ) \\ \end{align*}

[_linear]

3.146

7537

\begin{align*} x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\ \end{align*}

[_linear]

2.318

7538

\begin{align*} y^{\prime }&=2-\sqrt {2 x -y+3} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

2.577

7539

\begin{align*} y^{\prime }+\tan \left (x \right ) y+\sin \left (x \right )&=0 \\ \end{align*}

[_linear]

2.165

7540

\begin{align*} 2 y+y^{\prime }&=y^{2} \\ \end{align*}

[_quadrature]

1.385

7541

\begin{align*} y^{\prime }&=\left (2 x +y-1\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

6.071

7542

\begin{align*} x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

160.573

7543

\begin{align*} y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

4.720

7544

\begin{align*} y-2 x -1+\left (x +y-4\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6.583

7545

\begin{align*} 2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

30.281

7546

\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.709

7547

\begin{align*} \sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[NONE]

145.401

7548

\begin{align*} y \left (x -y-2\right )+x \left (-x +y+4\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15.806

7549

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.773

7550

\begin{align*} 3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

51.475

7551

\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+5} \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.037

7552

\begin{align*} 4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

157.172

7553

\begin{align*} y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\ \end{align*}

[[_linear, ‘class A‘]]

1.392

7554

\begin{align*} x^{3}-y+y^{\prime } x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_linear]

4.852

7555

\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (1\right ) &= -4 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7.768

7556

\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}

[[_linear, ‘class A‘]]

1.629

7557

\begin{align*} y^{\prime }-\frac {2 y}{x}&=\cos \left (x \right ) x^{2} \\ y \left (\pi \right ) &= 2 \\ \end{align*}

[_linear]

3.584

7558

\begin{align*} 2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\ y \left (1\right ) &= -2 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13.168

7559

\begin{align*} 2 \cos \left (2 x +y\right )-x^{2}+\left (\cos \left (2 x +y\right )+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_exact]

5.102

7560

\begin{align*} 2 x -y+\left (-3+x +y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

48.576

7561

\begin{align*} \sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

5.980

7562

\begin{align*} y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

6.469

7563

\begin{align*} y^{\prime }-4 y&=2 x y^{2} \\ y \left (0\right ) &= -4 \\ \end{align*}

[_Bernoulli]

3.131

7564

\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1}-y \\ y \left (2\right ) &= 3 \\ \end{align*}

[_linear]

2.641

7565

\begin{align*} y&=y^{\prime } x +2 {y^{\prime }}^{2} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.287

7566

\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.070

7567

\begin{align*} y^{\prime }&=2 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_quadrature]

4.362

7568

\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

26.995

7569

\begin{align*} y^{\prime }+a y&=Q \left (x \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

1.969

7570

\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.540

7571

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

14.721

7572

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.137

7573

\begin{align*} 2 y^{\prime \prime }+18 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.239

7574

\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

10.177

7575

\begin{align*} y^{\prime \prime }+4 y&=2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

9.967

7576

\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (3 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

79.876

7577

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

82.411

7578

\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

81.988

7579

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

75.483

7580

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

64.840

7581

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

49.654

7582

\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.415

7583

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.388

7584

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.158

7585

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.590

7586

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.321

7587

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.641

7588

\begin{align*} 6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.410

7589

\begin{align*} z^{\prime \prime }+z^{\prime }-z&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

6.783

7590

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.017

7591

\begin{align*} y^{\prime \prime }-y^{\prime }-11 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.046

7592

\begin{align*} 4 w^{\prime \prime }+20 w^{\prime }+25 w&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.173

7593

\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.398

7594

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.191

7595

\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.991

7596

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{3}} \\ \end{align*}

[[_2nd_order, _missing_x]]

1.188

7597

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= 9 \\ \end{align*}

[[_2nd_order, _missing_x]]

10.583

7598

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {25}{3}} \\ \end{align*}

[[_2nd_order, _missing_x]]

6.663

7599

\begin{align*} z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= -3 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.356

7600

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

[[_2nd_order, _missing_x]]

6.338